The mesoscopic conductance of disordered rings, its random matrix theory, and the generalized variable range hopping picture

Abstract

The calculation of the conductance of disordered rings requires a theory that goes beyond the Kubo-Drude formulation. Assuming "mesoscopic" circumstances the analysis of the electro-driven transitions show similarities with a percolation problem in energy space. We argue that the texture and the sparsity of the perturbation matrix dictate the value of the conductance, and study its dependence on the disorder strength, ranging from the ballistic to the Anderson localization regime. An improved sparse random matrix model is introduced to captures the essential ingredients of the problem, and leads to a generalized variable range hopping picture.

arXiv comment11 pages, 3 figures, improved version to be published as JPA/FTC

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Cited by in corpus (7)

• An Exactly Solvable Model for the Integrability-Chaos Transition in Rough Quantum Billiards
• Semilinear response for the heating rate of cold atoms in vibrating traps
• Random-matrix modeling of semi-linear response, the generalized variable range hopping picture, and the conductance of mesoscopic rings
• Quantum response of weakly chaotic systems
• Energy absorption by "sparse" systems: beyond linear response theory
• Non-equilibrium steady state of sparse systems
• "Weak Quantum Chaos" and its resistor network modeling